Advertisement

A Community-Aware Approach to Minimizing Dissemination in Graphs

  • Chuxu Zhang
  • Lu Yu
  • Chuang Liu
  • Zi-Ke Zhang
  • Tao Zhou
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10366)

Abstract

Given a graph, can we minimize the spread of an entity (such as a meme or a virus) while maintaining the graph’s community structure (defined as groups of nodes with denser intra-connectivity than inter-connectivity)? At first glance, these two objectives seem at odds with each other. To minimize dissemination, nodes or links are often deleted to reduce the graph’s connectivity. These deletions can (and often do) destroy the graph’s community structure, which is an important construct in real-world settings (e.g., communities promote trust among their members). We utilize rewiring of links to achieve both objectives. Examples of rewiring in real life are prevalent, such as purchasing products from a new farm since the local farm has signs of mad cow disease; getting information from a new source after a disaster since your usual source is no longer available, etc. Our community-aware approach, called constrCRlink (short for Constraint Community Relink), preserves (on average) \(98.6\%\) of the efficacy of the best community-agnostic link-deletion approach (namely, NetMelt \(^{+}\)), but changes the original community structure of the graph by only \(4.5\%\). In contrast, NetMelt \(^{+}\) changes \(13.6\%\) of the original community structure.

Keywords

Dissemination control in graph Community structure Graph mining 

Notes

Acknowledgements

This work was partially supported by Natural Science Foundation of China (Grant Nos. 61673151, 61503110 and 61433014), Zhejiang Provincial Natural Science Foundation of China (Grant Nos. LY14A050001 and LQ16F030006).

References

  1. 1.
    Blondel, V.D., Guillaume, J.-L., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in large networks. J. Stat. Mech. Theory Exp. 2008(10), P10008 (2008)CrossRefGoogle Scholar
  2. 2.
    Burt, R.S.: Structural Holes: The Social Structure of Competition. Harvard University Press, Cambridge (1992)Google Scholar
  3. 3.
    Chakrabarti, D., Wang, Y., Wang, C., Leskovec, J., Faloutsos, C.: Epidemic thresholds in real networks. ACM Trans. Inf. Syst. Secur. 10(4), 1 (2008)CrossRefGoogle Scholar
  4. 4.
    Chan, H., Akoglu, L., Tong, H.: Make it or break it: manipulating robustness in large networks. In: Proceedings of the 2014 SIAM International Conference on Data Mining, pp. 325–333. SIAM (2014)Google Scholar
  5. 5.
    Chen, C., Tong, H., Prakash, B.A., Eliassi-Rad, T., Faloutsos, M., Faloutsos, C.: Eigen-optimization on large graphs by edge manipulation. ACM Trans. Knowl. Discov. Data 10(4), 49 (2016)CrossRefGoogle Scholar
  6. 6.
    Fortunato, S.: Community detection in graphs. Phys. Rep. 486(3), 75–174 (2010)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Girvan, M., Newman, M.E.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. 99(12), 7821–7826 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Gruhl, D., Guha, R., Liben-Nowell, D., Tomkins, A.: Information diffusion through blogspace. In: Proceedings of the 13th International Conference on World Wide Web, pp. 491–501. ACM (2004)Google Scholar
  9. 9.
    Karrer, B., Levina, E., Newman, M.E.: Robustness of community structure in networks. Phys. Rev. E 77(4), 046119 (2008)CrossRefGoogle Scholar
  10. 10.
    Kuhlman, C.J., Tuli, G., Swarup, S., Marathe, M.V., Ravi, S.: Blocking simple and complex contagion by edge removal. In: 2013 IEEE 13th International Conference on Data Mining, pp. 399–408. IEEE (2013)Google Scholar
  11. 11.
    Kumar, R., Novak, J., Raghavan, P., Tomkins, A.: On the bursty evolution of blogspace. World Wide Web 8(2), 159–178 (2005)CrossRefGoogle Scholar
  12. 12.
    Lanczos, C.: An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. United States Government Press Office (1950)Google Scholar
  13. 13.
    Le, L.T., Eliassi-Rad, T., Tong, H.: MET: a fast algorithm for minimizing propagation in large graphs with small eigen-gaps. In: Proceedings of the 2015 SIAM International Conference on Data Mining, pp. 694–702. SIAM (2015)Google Scholar
  14. 14.
    Leskovec, J., Lang, K.J., Mahoney, M.: Empirical comparison of algorithms for network community detection. In: Proceedings of the 19th International Conference on World Wide Web, pp. 631–640. ACM (2010)Google Scholar
  15. 15.
    Nematzadeh, A., Ferrara, E., Flammini, A., Ahn, Y.-Y.: Optimal network modularity for information diffusion. Phys. Rev. Lett. 113(8), 088701 (2014)CrossRefGoogle Scholar
  16. 16.
    Pastor-Satorras, R., Vespignani, A.: Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86(14), 3200 (2001)CrossRefGoogle Scholar
  17. 17.
    Prakash, B.A., Chakrabarti, D., Faloutsos, M., Valler, N., Faloutsos, C.: Threshold conditions for arbitrary cascade models on arbitrary networks. In: 2011 IEEE 11th International Conference on Data Mining, pp. 537–546 (2011)Google Scholar
  18. 18.
    Rosvall, M., Bergstrom, C.T.: Maps of random walks on complex networks reveal community structure. Proc. Natl. Acad. Sci. 105(4), 1118–1123 (2008)CrossRefGoogle Scholar
  19. 19.
    Saha, S., Adiga, A., Prakash, B.A., Vullikanti, A.K.S.: Approximation algorithms for reducing the spectral radius to control epidemic spread. In: Proceedings of the 2015 SIAM International Conference on Data Mining, pp. 568–576. SIAM (2015)Google Scholar
  20. 20.
    Tong, H., Prakash, B.A., Eliassi-Rad, T., Faloutsos, M., Faloutsos, C.: Gelling, and melting, large graphs by edge manipulation. In: Proceedings of the 21st ACM International Conference on Information and Knowledge Management, pp. 245–254. ACM (2012)Google Scholar
  21. 21.
    Zhang, Y., Adiga, A., Saha, S., Vullikanti, A., Prakash, B.A.: Near-optimal algorithms for controlling propagation at group scale on networks. IEEE Trans. Knowl. Data Eng. 28(12), 3339–3352 (2016)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Alibaba Research Center for Complexity SciencesHangzhou Normal UniversityHangzhouChina
  2. 2.Department of Computer Science and EngineeringUniversity of Notre DameNotre DameUSA
  3. 3.King Abdullah University of Science and TechnologyJeddahSaudi Arabia
  4. 4.Big Data Research CenterUniversity of Electronic Science and Technology of ChinaChengduChina

Personalised recommendations